Edit multiple parts of tower mesh simultaneously
As the comments above indicate, the best way to do what I wanted is to create a circular array. 

What I did was:


Delete everything except one buttress and wall.
In object mode, select the remaining buttress and wall then in the Modifiers panel, click "Add Modifier" > "Array"
Press Shift+C > "Cursor to Centre" then Shift+A > "Empty" > "Plain Axes".
Reselect the buttress and wall then in the Modifiers panel, tick the "Add Offset" box, then click the box below that and select the empty created in the previous step, then untick the "Relative Offset" box and finally, change "Count" to the number of duplicates needed.
Reselect the created Empty then, in the transform box, change the Rotations until the clones are positioned correctly.
Make the required edits to the mesh.
When finished, in the Modifiers panel, click on "Apply".


Edit: The above are the instructions for Blender v2.49, which I was using at the time. For v2.79, the instructions are slightly different:


Delete everything except one buttress and wall.
In object mode, select the remaining buttress and wall then in the Modifiers panel (wrench button in Properties pane), click "Add Modifier" > "Array"
Press Shift+C then Shift+A > "Empty" > "Plain Axes".
Reselect the buttress and wall then in the Modifiers panel, tick the "Object Offset" box, then click the dropbox below that and select the empty created in the previous step, then untick the "Relative Offset" box and finally, change "Count" to the number of duplicates needed.
Reselect the created Empty then, in the transform box, change the Rotations until the clones are positioned correctly.
Make the required edits to the mesh.
When finished, in the Modifiers panel, click on "Apply".